Decision making for energy investments by using neutrosophic present worth analysis with interval-valued parameters

doi:10.1016/j.engappai.2020.103639

Engineering Applications of Artificial Intelligence

Volume 92, June 2020, 103639

https://doi.org/10.1016/j.engappai.2020.103639 Get rights and content

Abstract

Due to the increasing energy consumption of the world, new alternative energy sources are needed. The alternative energy resources can be classified into three categories such as fossil fuels energy resources, renewable energy resources, and nuclear energy resources. Solar energy is a very commonly used renewable energy resource for generating electricity and heating water. In this paper, establishing a solar energy system is handled as an investment analysis problem whose parameters are defined under uncertainty. Therefore, neutrosophic sets as a mean of dealing with uncertainty have been preferred to capture this vagueness and impreciseness. Neutrosophic sets are one of the extensions of intuitionistic fuzzy sets, which use an indeterminacy function unlike the other extensions of fuzzy sets. This paper proposes a new neutrosophic investment analysis method by using interval-valued parameters to evaluate solar energy systems. In the application section, three different types of solar energy systems are evaluated by the proposed method. It is observed that the proposed method presents big flexibility to experts and it gives effective and efficient results.

Introduction

Investors make critical decisions based on the relative profits and potential risks of investment alternatives. The main objective of this investment analysis is to choose the most suitable investment option for more profitability. Investment analyses involve some techniques using initial costs, annual cash flows, and salvage values over the estimated useful life of an investment. Some of these techniques are as follows: present worth analysis (PWA), future worth analysis, annual worth analysis, internal rate of return, benefit/cost ratio analysis, and rate of return analysis. PWA converts future cash flows to its equivalent present value, and then investment alternatives are evaluated as per their present values. PWA is one of the most used techniques because of its ease of calculation and understandability.

The recent developments in technology, rapid population growth and industrial developments have caused a great increase in world energy consumption. Due to this increase in energy consumption, research on new energy resources has gained great importance. The energy resources are grouped into three categories: fossil fuels, renewable resources and nuclear resources (Demirbas, 2000). Renewable energy is generated from natural processes and naturally replenished with time. The main renewable energy sources are hydropower, modern biomass, geothermal, solar, wind, and tidal energy (Demirbas, 2006).

Solar power is one of the most used renewable energy resources in comparison to other renewable energy resources. Solar energy can be used in anywhere with sunlight since it has flexibility and portability. Due to this feature, this energy resource plays a big role to meet our energy demands easily. The most common use of solar energy is electricity generation and domestic water heating by using solar radiation from the Sun through a variety of methods. In this paper, the main focus is given to electricity generation function of solar energy. The most frequently used methods for generating the electricity are; photovoltaic cells and solar thermal power plants (Fig. 1, Fig. 2). Solar panels consist of many photovoltaic cells, and they create opportunities for the individual power consumer to be involved in the production of power.

Photovoltaic cells can be manufactured from a variety of different materials in many ways. There are three types of Photovoltaic cells technologies that dominate the world market: monocrystalline silicon, polycrystalline silicon, and thin film. There are other two types of Photovoltaic cells named Higher efficiency Photovoltaic cells Technologies and emerging Photovoltaic cells technologies. The main focus of this paper is the first three types of Photovoltaic cells for producing solar panels, and with this respect detailed information about these solar panels is given in the application section.

Investment analysis parameters generally include uncertainty, vagueness and ambiguity. Therefore, it is hard to obtain exact data about these parameters. This situation makes decision-making process of investment alternative selection difficult for decision-makers. Fuzzy logic, developed by Zadeh (1965), provides a mathematical way to represent uncertainty, vagueness, and ambiguity. Fuzzy sets are classes of objects whose memberships are defined between 0 and 1 (Nicolas, 2015). Fuzzy sets present more comprehensive and better representation of reality than the classical sets binary representation (Kahraman et al., 2016a).

In recent years, fuzzy sets have been extended to new types in order to define the uncertainty in more detail. Type-2 fuzzy sets were introduced by Zadeh (1975). Interval-valued fuzzy sets were also introduced independently by Zadeh (1975), Grattan-Guiness (1975), and Sambuc (1975). Atanassov (1986) developed intuitionistic fuzzy sets (IFSs) including the membership value as well as the non-membership value. Yager (1986) introduced fuzzy multi-sets theory. Smarandache (1998) proposed neutrosophic sets (NS) by adding an independent indeterminacy-membership function to intuitionistic fuzzy sets. Garibaldi and Ozen (2007) proposed Nonstationary fuzzy sets that are evolved to handle uncertainties in fuzzy systems with reducing the computational burden of Type-2 sets. Hesitant fuzzy sets, developed by Torra (2010), are the extensions of regular fuzzy sets that handle the situations where a set of values are possible for the membership of a single element.

Neutrosophic logic is based on neutrosophy. Neutrosophic sets try to measure the truthiness (T), indeterminacy (I) and falsity (F) degrees of each element in a set. In other words, each proposition is estimated to have a percentage of truth in subset T, a percentage of indeterminacy in subset I, and a percentage of falsity in subset F. Truthiness and falsity correspond to membership and non-membership as in intuitionistic fuzzy sets. Differently, indeterminacy value is firstly defined by neutrosophic sets in the literature. Neutrosophic sets carry more information than other fuzzy sets by using “indeterminacy” value. In a neutrosophic set, the sum of these parameters T, I, and F, which are $\in]^{-} 0, 1^{+} [$ must satisfy the condition $^{-} 0 \leq s u p T_{A} (x) + s u p I_{A} (x) + s u p F_{A} (x) \leq 3^{+}$ . Since it is hard to utilize these definitions in practical problems, single valued neutrosophic sets were proposed by Wang et al. (2010). They identified the components of neutrosophic sets as follows: $T_{A} (x), I_{A} (x), F_{A} (x) \in [0, 1]$ and $0 \leq T_{A} (x) + I_{A} (x) + F_{A} (x) \leq 3$ .

In this study, solar energy panel investment alternatives were evaluated by using neutrosophic sets and interval-valued parameters. Interval-valued parameters allow experts to make more flexible appointments to alternatives. Arithmetic operations with interval numbers are the basis of the operations with interval-valued parameters under fuzziness. Hence, the arithmetic operations are presented with interval numbers in a separate section in this paper.

In the literature, there have been many studies on fuzzy engineering economics models, especially about fuzzy present worth analysis. Ward (1985) developed the first fuzzy PWA technique in the literature. Buckley (1987) developed the PWA by using both fuzzy cash flows and fuzzy interest rates. Chiu and Park (1994) developed fuzzy PWA, and he used fuzzy cash flows and fuzzy interest rates with triangular fuzzy numbers. Kuchta (2000) defined fuzzy PWA by using interval-valued fuzzy numbers to evaluate investment alternatives. Karsak and Tolga (2001) presented a fuzzy present value model in order to evaluate the advanced manufacturing system investments. Nachtmann and Needy (2001) proposed PWA technique by using Type-1 fuzzy sets, and they evaluated knowledge information investment alternatives. Kahraman et al. (2002) developed fuzzy PWA formulas, and they expanded the examined cash flows to geometric and trigonometric cash flows. Tercenño et al. (2003) presented fuzzy PWA formula to select portfolios of tangible investments. Dimitrovski and Matos (2008) proposed the fuzzy PWA for cash flows with correlated and uncorrelated cash flows. UçaI and Kuchta (2011) presented a project scheduling method to maximize the fuzzy present worth value of investment alternatives. Kahraman et al. (2015a) used triangular hesitant fuzzy numbers to develop fuzzy PWA formulas. Bhattacharyya et al. (2011) developed fuzzy present value analysis formulas for selection research and development projects. Kahraman et al. (2015b) developed fuzzy PVA formulas based on intuitionistic and HFSs, and they used triangular hesitant fuzzy data, triangular intuitionistic fuzzy data, interval-valued hesitant data, and interval-valued intuitionistic fuzzy data in investment analysis problem. Kahraman et al. (2016b) used interval-valued intuitionistic fuzzy numbers to develop PWA for the investment’s alternative evaluation. Kahraman et al. (2017) developed fuzzy PWA by using Pythagorean fuzzy set for the investment’s alternative evaluation. Aydın et al. (2018) developed neutrosophic PWA technique to evaluate lathe investment alternatives.

In this paper, unlike the other studies, a new neurosophic PWA method is presented with interval parameters for the first time in the literature. The experts defined the possible parameter values with intervals values and assigned the single valued neutrosophic T, I, and F values to these parameters. Thus, this evaluation process provides larger flexibility in handling the possible values of parameters and captures the vagueness in experts’ minds. The most important contribution of this study to the literature is the usage of both interval valued parameters and single valued neutrosophic numbers together in investment analysis problems. A comparative analysis is presented by using both a neutrosophic annual worth analysis and intuitionistic fuzzy present worth analysis.

The rest of the paper is organized as follows: Arithmetic operations with interval numbers are given in Section 2. Preliminaries for single valued neutrosophic sets are given in Section 3. The single valued PWA method with interval-valued parameters is given in Section 4. A case study and comparative analyses are presented in Section 5, and conclusions are given in the last section.

Section snippets

Arithmetic operations with interval numbers

Consider a set $X$ and a set $I X$ of subset of $X$ . $I X$ is a set of wrappers for $X$ if $X$ , and each singleton of $X$ belongs to $I X$ and if $I X$ is closed by intersection. In interval analysis, the wrappers to be used are intervals when dealing with $R$ and axis-aligned boxes when dealing with $R^{n}$ Jaulin et al., 2001, Wang and Tsai, 2018.

Let $a, b \in R$ such that $a \leq_{R} b$ . A classical interval number $[a, b]$ is a closed and bounded nonempty real interval, that is, $[a, b] = \{x \in R |a \leq_{R} x \leq_{R} b\}$ where $a = \min ([a, b])$ and $b = \max ([a, b])$ are called the

Preliminaries for single valued neutrosophic sets

Let X be a space of objects, with a generic element in X denoted by x. A neutrosophic set A in X is characterized by a truth-membership function $T_{A} (x)$ an indeterminacy membership function $I_{A} (x)$ and a falsity-membership function $F_{A} (x)$ . The functions $T_{A} (x)$ , $I_{A} (x)$ and $F_{A} (x)$ are real standard or nonstandard subsets of $]^{-} 0, 1^{+} [$ that is $T_{A} (x) : X \to]^{-} 0, 1^{+} [, I_{A} (x) : X \to]^{-} 0, 1^{+} [, F_{A} (x) : X \to]^{-} 0, 1^{+} [$ . There is no restriction on the sum of $T_{A} (x)$ , $I_{A} (x)$ and $F_{A} (x)$ , so $^{-} 0 \leq {s u p T_{A} (x)} + {s u p I_{A}} (x) + {s u p F_{A}} (x) = 3^{+}$ .

Smarandache (1998)

Single valued neutrosophic present worth analysis with interval-valued parameters

In this section, the steps of single valued neutrosophic present worth (SVNPW) technique are given. The proposed formulas can utilize interval-valued parameters and experts’ neutrosophic evaluations for these parameter values. In this paper, a new neutrosophic min–max union operator was proposed to aggregate experts’ opinions. Another feature that distinguishes the proposed method from the other methods is that possible interval-valued parameters values and their corresponding neutrosophic T, I

Case study: Decision making in energy investment in Turkey

According to the Solar Energy Map (SEM) of Turkey prepared by Ministry of Energy and Natural Resources, it has been determined that the total annual insulation time is 2,741 h (a total of 7,5 h per day), and the total solar energy derived per year is 1,527 kWh/m2 per year (total 4,18 kWh/m2 per day). The total established solar collector area within Turkey as of 2018 was calculated as being close to 20,200,000 m2. Furthermore, in 2018, close to 876,720 TEP (Tonnes Equivalent to Petrol) heat

Conclusion

Due to the increasing energy consumption of the world, orientation towards alternative energy sources has become a significant issue. Renewable energy resources are the most preferred sources because they are inexhaustible and do not give any harm to the environment. In recent years, many technological studies have been carried out in order to get benefits from renewable energy sources. Solar energy panels use a special process of converting photons to electrons to generate a current by making

CRediT authorship contribution statement

Serhat Aydın: Investigation, Methodology, Software, Writing - review & editing. Cengiz Kahraman: Methodology, Visualization, Investigation, Conceptualization, Review. Mehmet Kabak: Visualization, Investigation, Conceptualization, Review.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (36)

AtanassovK.T.
Intuitionistic fuzzy sets
Fuzzy Sets and Systems
(1986)
BhattacharyyaR. et al.
Fuzzy R & D portfolio selection of interdependent projects
Comput. Math. Appl.
(2011)
BuckleyJ.J.
The fuzzy mathematics of finance
Fuzzy Sets and Systems
(1987)
IshibuchiH. et al.
Multiobjective programming in optimization of the interval objective function
European J. Oper. Res.
(1990)
KahramanC. et al.
Interval-valued intuitionistic fuzzy investment analysis: application to CNC lathe selection
Int. Feder. Autom. Control
(2016)
KahramanC. et al.
Capital budgeting techniques using discounted fuzzy versus probabilistic cash flows
Inform. Sci.
(2002)
KuchtaD.
Fuzzy capital budgeting
Fuzzy Sets and Systems
(2000)
ZadehL.A.
Fuzzy sets
Inf. Control
(1965)
ZadehL.A.
The concept of a linguistic variable and its application to approximate reasoning-1
Inform. Sci.
(1975)
AydınS. et al.
Evaluation of investment alternatives using present value analysis with simplified neutrosophic sets
Eng. Econ.
(2018)

ChiuC.Y. et al.

Fuzzy cash flow analysis using present worth criterion

Eng. Econ.

(1994)

DemirbasA.

Recent advances in biomass conversion technologies

Energy Educ. Sci. Technol.

(2000)

DemirbasA.

Global renewable energy resources

Energy Sources A: Recov. Util. Environ. Effects

(2006)

DimitrovskiA. et al.

Fuzzy present worth analysis with correlated and uncorrelated cash flows

GangopadhyayU. et al.

State of Art of Solar Photovoltaic TechnologyHindawi Publishing Corporation Conference Papers in Energy

(2013)

GaribaldiJ.M. et al.

Uncertain fuzzy reasoning: A case study in modelling expert decision making

IEEE Trans. Fuzzy Syst.

(2007)

Grattan-GuinessI.

Fuzzy membership mapped onto interval and many-valued quantities

Z. Math. Logik. Grundladen Math.

(1975)

JaulinL. et al.

Applied Interval Analysis

(2001)

Cited by (11)

A new model for resilient-sustainable energy project portfolio with bi-level budgeting and project manager skill utilization under neutrosophic fuzzy uncertainty: A case study
2024, Engineering Applications of Artificial Intelligence
One of the most important areas of infrastructure projects that can contribute to the goals of sustainable development is the energy sector. Forming the right set of energy projects can lead to developing a sustainable environment. Another important aspect is the resilience of energy projects. This paper introduces a novel approach that simultaneously considers resilience and sustainability in forming energy project portfolios. In the first part, the relative importance of each project is computed under a triangular neutrosophic (TN) environment. This approach keeps the vagueness of data while evaluating projects versus resiliency and sustainability criteria. In the second part, an interval mathematical model is presented to maximize the total value of the selected portfolio while addressing bi-level budgeting and skill utilization. In this study, uncertainty is expressed in a hybrid way which enhances the flexibility of computations in addition to providing experts with more freedom in expressing their opinions. To present the application of this method, data from an existing case study has been used, and the process has been implemented step by step. This application demonstrates the importance of addressing resilience and sustainability in energy projects. Moreover, it shows the benefits of applying a hybrid solution approach in presenting the vagueness of energy projects in addition to assigning the budget in a bi-level process.
Information measures based on similarity under neutrosophic fuzzy environment and multi-criteria decision problems
2023, Engineering Applications of Artificial Intelligence
The neutrosophic fuzzy set (NF-set) is a unique hybrid structure that combines the essence of the fuzzy and neutrosophic sets. It is an effective mathematical tool for dealing with indeterminate and inconsistent information in situations where the data are imprecise or vague. This paper defines the concepts of similarity-based information measures, including entropy and cross-entropy, between NF-sets. It is the first time these concepts have been introduced since the NF-sets were defined. We provide their interesting properties through well-proven theorems. In addition, we also propose a novel and efficient algorithm to make multi-criteria decision(s) using these information measures with a clear step-by-step illustration. It overcomes the limitations of the original algorithm when evaluating the criteria in two aspects: qualitative and quantitative. A real-world experiment is then conducted to assist students in choosing the optimal subject group(s) for the Vietnamese national high school graduation examination. Experimental results show that our method outperforms the previous original method when giving recommendations with sixteen correct cases, three acceptable cases, and one noisy case out of twenty real-life cases. Finally, the experimental results are presented visually, analyzed rigorously, and discussed carefully, intending to verify the validity and feasibility of the proposed algorithm. The Python source code for experiments is publicly available on Github.
A PCA-based fuzzy tensor evaluation model for multiple-criteria group decision making
2023, Applied Soft Computing
Citation Excerpt :
Interval-valued neutrosophic fuzzy sets (IVNFS), due to their flexible nature, are the have been used quite frequently used by researchers for evaluating the solutions under uncertain scenario. Recent studies on IVNFNs in the literature can be found in [32–34]. The aggregation operators of IVNFS have drawn much attention and have become a relevant research topic in the MCGDM field.
Multiple-criteria group decision-making (MCGDM) problems mainly consist of multiple factors and multiple Decision Makers (DMs) or Users, for which dimension extension is necessary when considering all the entries of DMs together. Tensor, a generalized form of a matrix, displays a multi-way array item, which is the most suitable and practical way to represent high-dimensional data without losing any information. In this paper, we first reduce the dimension through Principal Component Analysis (PCA), which helps consider the most-informative criteria. Then, we reintroduced the tensor as a fuzzy-form tensor for the MCGDM problem because of user information uncertainty. We choose Interval-valued Neutrosophic Fuzzy numbers (IVNFNs) as the basis for the tensor form because of their ability to distinguish between truth, indeterminacy, and falsity in the data. Lastly, a Generalized Interval-valued Neutrosophic Fuzzy Weighted Geometric (GIVNFWG) operator is defined. Moreover, a generalized framework for fuzzy-form tensors for high-dimensional MCGDM problems is proposed. The feasibility and efficiency of this proposed process is illustrated for a real-world MCGDM problem of ranking the most efficient Third Party Reverse Logistics Partners (3PRLPs), i.e., recycled fiber-based paper mills for the packaging industry. The obtained results are according to the experts and are validated using sensitivity analysis. This analysis facilitates in assessing the impact on the overall ranking performance of 3PRLPs by considering various combinations of environment and technological sub-criteria.
Assessing IoT challenges in supply chain: A comparative study before and during- COVID-19 using interval valued neutrosophic analytical hierarchy process
2022, Journal of Business Research
Citation Excerpt :
However, a recent approach of using interval-valued neutrosophic sets (IVN) (Wang, Smarandache, Sunderraman, & Zhang, 2005) has not been widely implemented in real-life cases. The studies include using neutrosophic sets with interval-valued parameters to assess solar energy systems (Aydın, Kahraman, & Kabak, 2020) using the IVN-AHP to evaluate the selection of alternative energy sources (Bolturk & Kahraman, 2018) to name a few. This study is the first attempt to use IVN-AHP for the evaluation of IoT challenges.
Although the Internet of Things (IoT) has spawned a new breed of smart factories within supply chains, the latest pandemic has ushered in unparalleled supply chain disturbances. Following the challenges identified in the literature, we interview top experts to evaluate the significance of these challenges. We apply a multi-criteria decision analysis (MCDA) tool, analytical hierarchy process (AHP) in combination with interval-valued neutrosophic numbers (IVN). The critical part of this research is that we also perform a comparative analysis by focusing on before- and during- the pandemic periods individually to better assess the impact of the latest pandemic on the IoT challenges. Our study also includes a comprehensive, systematic literature review to bring the readers up-to-date.
A novel similarity measure in intuitionistic fuzzy sets and its applications
2022, Engineering Applications of Artificial Intelligence
Citation Excerpt :
These theories have their own advantages in dealing with uncertain information. Therefore, researchers have applied those theories to various fields, such as decision making (Aydın et al., 2020; Gao et al., 2020a; Liao et al., 2021), target classification (Luo and Zhang, 2020; Geramian and Abraham, 2021; Fu et al., 2020), clustering problem (Egrioglu et al., 2020; Budwong et al., 2021; Ding et al., 2021) and other mixed areas (Lopes et al., 2020; Ma et al., 2021; Solanki et al., 2021; Gao et al., 2020b). Since IFS were proposed, similarity measure in the IFSs has been studied, such as Chen firstly defined the similarity measure between IFSs (Chen, 1995).
Intuitionistic fuzzy set (IFS) is a classical branch of fuzzy set, which has advantage to deal with uncertain problems. In IFS, similarity measure is an important fundamental concept, it is used to measure consistency between different intuitionistic fuzzy sets (IFSs) and becomes a key parameter in fuzzy decision system. However, the previous methods of similarity measure do not take enough account the effect of hesitancy degree on membership degree and non-membership degree, so that produce counterintuitive results when measuring similarity. Hence, in this paper, a new similarity measure of IFS is presented. The effect of hesitancy degree on similarity measure is fully considered in the proposed method and some properties also haven been discussed to prove the reasonable of proposed method. Meanwhile, some numerical examples are analyzed to illustrate characteristics of proposed similarity measure in detail. Further, the experiments of target classification and clustering problem demonstrate effectiveness and superiority of proposed similarity measure in the environment of expert assessments and data set.
Process mining technology selection with spherical fuzzy AHP and sensitivity analysis
2021, Expert Systems with Applications
Citation Excerpt :
Many factors affect the selection decision, such as cost, training, return on investment and operational support. Hence the selection of suitable technology is a multi-criteria problem which considers several criteria and evaluations from different decision-makers (Kahraman, Oztaysi, Onar, & Dogan, 2018; Donyatalab, Seyfi-Shishavan, Farrokhizadeh, Kutlu Gündoğdu, & Kahraman, 2020; Aydin, Kahraman, & Kabak, 2020). A multi-criteria decision-making (MCDM) concentrates on challenges with discrete decision spaces and evaluates alternatives.
Process mining (PM) supports organizations by improving their processes using event log data collected from information technology systems. Its primary purposes are discovering actual process models, monitoring and comparing actual and desired workflows, and enhancing processes by considering the discovered model and desired flow. Because process mining gains attraction day by day, various technology companies developed process mining tools to support organizations managing their business processes with data science. Technology selection is a complicated multi-criteria decision-making (MDCM) problem under several criteria and experts’ evaluation, including uncertainty and subjectivity. Spherical fuzzy set is a powerful concept to cope with uncertainty by presenting a wider decision-making area and identifying hesitancy. A fuzzy MDCM approach based on spherical fuzzy AHP is offered in this study to manage the problem of selecting process mining technology under uncertain and ambiguous conditions. Then, one-at-a-time sensitivity analysis is applied to reduce the decision-makers’ subjectivity. This study results in that Price, Process Discovery, Process Analysis&Analytics are the most relevant criteria to decide PM technology. It is interesting that even although Operational Support is one of the less important criteria, it may change the decision on selecting the best PM technology.

View all citing articles on Scopus

View full text

Decision making for energy investments by using neutrosophic present worth analysis with interval-valued parameters

Abstract

Introduction

Section snippets

Arithmetic operations with interval numbers

Preliminaries for single valued neutrosophic sets

Single valued neutrosophic present worth analysis with interval-valued parameters

Case study: Decision making in energy investment in Turkey

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Fuzzy Sets and Systems

Comput. Math. Appl.

Fuzzy Sets and Systems

European J. Oper. Res.

Int. Feder. Autom. Control

Inform. Sci.

Fuzzy Sets and Systems

Inf. Control

Inform. Sci.

Evaluation of investment alternatives using present value analysis with simplified neutrosophic sets

Eng. Econ.

Fuzzy cash flow analysis using present worth criterion

Eng. Econ.

Recent advances in biomass conversion technologies

Energy Educ. Sci. Technol.

Global renewable energy resources

Energy Sources A: Recov. Util. Environ. Effects

Fuzzy present worth analysis with correlated and uncorrelated cash flows

State of Art of Solar Photovoltaic TechnologyHindawi Publishing Corporation Conference Papers in Energy

Uncertain fuzzy reasoning: A case study in modelling expert decision making

IEEE Trans. Fuzzy Syst.

Fuzzy membership mapped onto interval and many-valued quantities

Z. Math. Logik. Grundladen Math.

Applied Interval Analysis